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radical

Defines: 
radicand, index, radical expression
Synonym: 
radical symbol
Type of Math Object: 
Definition
Major Section: 
Reference

Mathematics Subject Classification

30-00 no label found12D99 no label found00A05 no label found

Comments

It amazes me some of the things that PM is still missing. Hip-hip hurray for Warren for adding this entry!

Lisa

Thanks Lisa. I definitely appreciate your encouragement. :-)

As for amazement at what PM is still missing, feel free to file requests. I check those pretty often. The area entry was created as a result of a request.

Warren

I have come across a dilemma in the entry to which I am attaching this post (radical).

The user pahio has informed me that one must use single quotes around words that are translations (such as root is within this entry). Typing this as `root' looks magnificent in page images mode, but not so hot in html mode. Instead, typing this as 'root' looks acceptable in html mode, but looks dumb in page images mode.

Does anyone know of a compromise that looks acceptable in both viewing modes and allows for internal linking?

Wkbj79 wrote:
> The user pahio has informed me that one must use single
> quotes around words that are translations (such as root is
> within this entry). Typing this as `root' looks magnificent
> in page images mode, but not so hot in html mode.

Personally, I think `root' looks better than 'root' in HTML
mode, but I might just be weird.

The fact that `root' looks odd in HTML mode is a bug (reported long ago). It will probably be fixed eventually.

But I don't see why you should put the word in quotes anyway. I would put it in italics.

Yes, italics seems like a good way to get out of this dilemma.

> Yes, italics seems like a good way to get out of this dilemma

... but contradicts the linguistic procedure :)
(all words and sentences of the object language are italized).

Jussi

> As for amazement at what PM is still missing, feel free to file requests. I check those pretty often. The area entry was created as a result of a request.

I was just saying. I don't know some of these stuff is missing until I see a new entry on it and then I'm all like, "There wasn't an entry on this before?" Some time ago, I don't remember who, said that maybe we should review some new math encyclopedia that's come out and identify all the topics PM doesn't have. I don't know if there's been any follow-up on that.

> I don't know some of these stuff is missing until I see a new entry on it and then I'm all like, "There wasn't an entry on this before?"

Quite a few of the objects that I add are along these lines. Mainly, after looking at an entry, I might spot some mathematical concept and ask myself, "Now why isn't this linking somewhere?" When I get the time, I do some digging around to see if it should actually link somewhere. If I can't find anything, then I create the object myself.

"Radical" is a case in point. Occurrences of "radical" were always linking (sometimes erroneously to one of the other five or so entries that define radical), but I stumbled across an entry in which "radicand" was not linking. It seemed pretty clear that no one had yet supplied the most elementary definition of radical.

In fact, a similar situation just occurred. In CWoo's entry "techniques in mathematical proofs", I noticed that the phrase "right inverse" was not linking properly. (It was linking to "right angle" and "inverse", respectively.) Again, after some digging, I finally decided to add "inverses in rings" in which I define a right inverse (among other things).

> Some time ago, I don't remember who, said that maybe we should review some new math encyclopedia that's come out and identify all the topics PM doesn't have. I don't know if there's been any follow-up on that.

Not that I am aware of, but this sounds like a good idea.

> Mainly, after looking at an entry, I might spot some mathematical concept and ask myself, "Now why isn't this linking somewhere?"

Ooh, I got one of those! In connection to the Erd\H{o}s-Straus conjecture, lowest common denominator, sometimes called least common denominator. The entry Fraction does mention how to compute the LCD, and it even has "lowest terms" in its Also defines: field.

> Ooh, I got one of those!

Nice to see someone get excited around here. :-)

> In connection to the Erd\H{o}s-Straus conjecture, lowest common denominator, sometimes called least common denominator. The entry Fraction does mention how to compute the LCD, and it even has "lowest terms" in its Also defines: field.

If you are going to create an entry on LCD, you may want to take a look at an entry (if it exists) on LCM. After all, a lowest common denominator is just the LCM of all of the denominators. On the other hand, separate entries may be appropriate, since LCM's are not necessarily connected to fractions, whereas LCD's must be.

> Some time ago, I don't remember who, said that maybe we should review some new math encyclopedia that's come out and identify all the topics PM doesn't have. I don't know if there's been any follow-up on that.

It was akrowne (Aaron) who said that:

http://planetmath.org/?op=getmsg&id=14565

I believe that such a search of other encyclopedia would useless, or futile excercise. WHY? Well, I am also editor in Wikipedia, and what is good in Wikipedia is that everybody creates entries on what he likes, on what is his interest, and on what he has spent say a lot of time of "reading, studying, and deeper digging". So I believe it is better if mathematicians here in PlanetMath just write on topic where they are involved, and create entries on all kind of topics and on subjects that may look minor now, but could be of great interest later. Paid encyclopedia cannot achieve this variety of topics covered.

One more comment concerning the entries that I have opened, and the curiosity on my personality i.e. whether I am sockpuppet. I have opened entries in math logic, which are based on my work in the last 3 years, indeed nothing is yet published it is only in draft form. My study was from Kleene "Math Logic", then after reading the whole book I studied Podnieks "Godel and around" hypertextbook, which I recommend for everybody involved in discussions on math logic. The main issue is the application of the theory to AI and mind, and I was trying to understand what sir Roger Penrose wanted to say in his 2 books on the subject. Well, surprizingly or not, Penrose makes a lot of severe basic errors, and what comes as main conclusions is that there is at least theoretical possibility that mind process is a kind of inconsistent algorithm, that operates in some logic that creates inconsistencies, but does not generalize the contradictions for all formulas i.e. weakened logic in which the axiom "from inconsistency follows everything" is false (i.e. its negation is true axiom, or theorem). So this lead me at least theoretically to think over the possibility for some semi-inconsistent logic, paradoxist logic, etc. and check whether these topics are of some interest or will turn out to be futile excercise. So one obvious candiate is NEUTROSOPHY of Smarandache, and studying the Smarandache n-structures, etc.

I tell this story for one reason - I have posted two entries on Smarandache, and immediately there was protest as if I have posted something extremely stupid. Indeed currently there is a biased entry on Smarandache where he is described as an evil, whose only purpose is to play idendity games with people.
PLEASE RECONSIDER YOUR ATTITUDE TOWARDS CREATION OF ENTRIES - LET EVERYBODY OPEN ENTRIES ON WHAT HE UNDERSTANDS BETTER.
And please do NOT open entries on topics that you don't understand or feel yourself incompetent to reply. Simply coping a topic from other encyclopedia is likely to put you in such position where the one who created the entry will be not able to reply to subtle questions on the topic.

Checking and copying other encyclopedias is futile activity.
Mathematics is excersice of mind, and product of mind, that is why it is better if one posts his own original ideas, in the context of what he already knows, in an environment where everybody can check them out :-)

> And please do NOT open entries on topics that you don't understand or feel yourself incompetent to reply. Simply copying a topic from other encyclopedia is likely to put you in such position where the one who created the entry will be not able to reply to subtle questions on the topic.

I definitely agree with this.

> Checking and copying other encyclopedias is futile activity.

I do not think we are seeing eye to eye here. If I remember correctly, the reason that akrowne proposed looking at the encyclopedia was so that we could see concepts they defined that we were missing. It would actually be possible for us to use their list of entries to come up with ideas to add to PM without even looking at a single article in the other encyclopedia. I definitely agree that copying is a bad idea, but not necessarily checking.

I want to highlight part of dankomed post, since his words describe exactly how I feel about Planetmath.

dankomed said:
>I believe that such a search of other encyclopedia would useless, or futile excercise. WHY? Well, I am also editor in Wikipedia, and what is good in Wikipedia is that everybody creates entries on what he likes, on what is his interest, and on what he has spent say a lot of time of "reading, studying, and deeper digging". So I believe it is better if mathematicians here in PlanetMath just write on topic where they are involved, and create entries on all kind of topics and on subjects that may look minor now, but could be of great interest later. Paid encyclopedia cannot achieve this variety of topics covered.

>And please do NOT open entries on topics that you don't understand or feel yourself incompetent to reply. Simply coping a topic from other encyclopedia is likely to put you in such position where the one who created the entry will be not able to reply to subtle questions on the topic.

> I want to highlight part of dankomed post, since his words
> describe exactly how I feel about Planetmath.

Me too.

> >And please do NOT open entries on topics that you don't
> understand or feel yourself incompetent to reply. Simply
> coping a topic from other encyclopedia is likely to put you
> in such position where the one who created the entry will be
> not able to reply to subtle questions on the topic.

And the same goes for adopting entries.

> Well, I am also editor in Wikipedia, and what is good in Wikipedia is that everybody creates entries on what he likes, on what is his interest, ... So I believe it is better if mathematicians here in PlanetMath just write on topic where they are involved, and create entries on all kind of topics and on subjects that may look minor now, but could be of great interest later.
>

I don't remember where I read that Wikipedia has more info on the Dominion War of the last season of Star Trek: Deep Space Nine than it has on the First Congo War. Though in all fairness, we also have to ask: which of these is more likely to be looked up?

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